FRACTIONAL CALCULUS AND APPLIED ANALYSIS（FCAA，在世界数据库中缩写为 FRACT. CALC. APPL. ANAL. 或 FRACT CALC APPL ANAL）是一本专门研究数学分析（微积分）重要分支的理论和应用的国际期刊，其中微分和积分可以是任意的非整数顺序。其内容的高标准由杰出的编辑委员会成员和受邀的外部审稿人的专业知识保证，并由最近取得的影响因子 (JIF) 和影响范围 (SJR) 的高值证明，使期刊跻身榜首THOMSON REUTERS 和 SCOPUS 的排行榜。

Fractional Calculus and Applied Analysis (FCAA), abbreviated as FRACT. CALC. APPL. ANAL. or FRACT CALC APPL ANAL in global databases, is an international journal dedicated to the theory and applications of an important branch of mathematical analysis (calculus), focusing on derivatives and integrals of arbitrary non-integer orders. The high standards of the journal are ensured by the expertise of an outstanding editorial board and invited external reviewers, and its recent high values in impact factor (JIF) and scope of influence (SJR) demonstrate its leading position in the rankings of THOMSON REUTERS and SCOPUS.

《Fractional Calculus and Applied Analysis》（FCAA，世界数据库中缩写为 FRACT. CALC. APPL. ANAL. 或 FRACT CALC APPL ANAL）是一本国际期刊，专注于数学分析（微积分）这一重要分支的理论与应用，研究内容涉及任意非整数阶的微分与积分。期刊的高标准由杰出的编辑委员会成员和受邀的外部审稿人的专业知识所保证，且其最近获得的影响因子（JIF）和影响范围（SJR）均显示出较高的值，使其在THOMSON REUTERS和SCOPUS的排行榜中名列前茅。

Fractional Calculus and Applied Analysis

Abstract We propose an alternative definition of a mixed partial derivative in the Caputo sense for functions of two variables defined on the rectangle $$P=[0,a]\times [0,b]$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>P</mml:mi> <mml:mo>=</mml:mo> <mml:mo>[</mml:mo> <mml:mn>0</mml:mn> <mml:mo>,</mml:mo> <mml:mi>a</mml:mi> <mml:mo>]</mml:mo> <mml:mo>×</mml:mo> <mml:mo>[</mml:mo> <mml:mn>0</mml:mn> <mml:mo>,</mml:mo> <mml:mi>b</mml:mi> <mml:mo>]</mml:mo> </mml:mrow> </mml:math> ( $$a&gt;0, b&gt;0$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>a</mml:mi> <mml:mo>&gt;</mml:mo> <mml:mn>0</mml:mn> <mml:mo>,</mml:mo> <mml:mi>b</mml:mi> <mml:mo>&gt;</mml:mo> <mml:mn>0</mml:mn> </mml:mrow> </mml:math> ). We give an integral representation of functions possessing such a derivative. Moreover, we study the existence and uniqueness of a solution, as well as the Ulam–Hyers type stability of a fractional counterpart of a nonlinear continuous Goursat-Darboux system described by the introduced Caputo derivative. This paper is a continuation of our paper [R. Kamocki, C. Obczyński, On the single partial Caputo derivatives for functions of two variables , Periodica Mathematica Hungarica 87(2), (2023), 324–339].

Rafał Kamocki

Cezary Obczyński

On a mixed partial Caputo derivative and its applications to a hyperbolic partial fractional differential equation

关于混合部分Caputo导数及其在双曲部分分数阶微分方程中的应用

Dariusz Idczak

A time-space fractional parabolic type problem: weak, strong and classical solutions

时间-空间分数阶抛物型问题：弱解、强解与经典解

Cornelia Mihaila

Brian Seguin

A definition of fractional k-dimensional measure: bridging the gap between fractional length and fractional area

分数k维测度的定义：弥合分数长度与分数面积之间的差距

Tian Feng

YangQuan Chen

A collection of correct fractional calculus for discontinuous functions

不连续函数正确分数阶微积分集

Eudes M. Barboza

Olímpio H. Miyagaki

Fábio R. Pereira

Cláudia R. Santana

Hardy–Hénon fractional equation with nonlinearities involving exponential critical growth

带有涉及指数临界增长非线性的Hardy-Hénon分数阶方程

Abstract In this paper, we investigate the optimal control of a semi-linear fractional PDEs involving the spectral diffusion operator, or the realization of the integral fractional Laplace operator with the zero Dirichlet exterior condition, both of order s with $$s\in (0,1)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>s</mml:mi> <mml:mo>∈</mml:mo> <mml:mo>(</mml:mo> <mml:mn>0</mml:mn> <mml:mo>,</mml:mo> <mml:mn>1</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> . The state equation contains a non-smooth nonlinearity, and the objective functional is convex in the control variable but contains non-smooth terms. As the mappings involved may not be Gâteaux differentiable, we use a regularization technique to regularize these nonlinear terms, aiming to obtain Gâteaux differentiable mappings. By employing this regularization technique, we are able to derive the first-order optimality condition for the regularized control problem by using the associated adjoint system. Furthermore, we conduct a limit analysis on the regularized term resulting in an optimality system for the non-smooth problem of C-stationary type. Subsequently, we establish a primal optimality condition, specifically B-stationarity. Under the assumption of “constraint qualification”, we derive the strong stationarity conditions for the non-smooth optimization problem with control constraints and establish the equivalence between B-stationarity and strong stationarity conditions.

Cyrille Kenne

Gisèle Mophou

Mahamadi Warma

Strong stationarity for non-smooth control problems with fractional semi-linear elliptic equations in dimension $$N\le 3$$

非光滑控制问题中分数阶半线性椭圆方程在维数$$N\le 3$$下的强平稳性

Abbreviation	Fract Calc Appl Anal
Journal Impact	2.52
Quartiles(Global)	MATHEMATICS, INTERDISCIPLINARY APPLICATIONS(Q2)

ISSN	1311-0454, 1314-2224
h-index	64

Publication Information	Publisher: Springer International Publishing AG，Publishing cycle: ，Journal Type: journal，Open Access Journals: No
Basic data	Year of publication: 2011，Proportion of original research papers: 96.77%，Self Citation Rate:12.00%， Gold OA Rate: 18.95%

Fractional Calculus and Applied Analysis

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On a mixed partial Caputo derivative and its applications to a hyperbolic partial fractional differential equation

A time-space fractional parabolic type problem: weak, strong and classical solutions

A definition of fractional k-dimensional measure: bridging the gap between fractional length and fractional area

A collection of correct fractional calculus for discontinuous functions

Hardy–Hénon fractional equation with nonlinearities involving exponential critical growth

A time-space fractional parabolic type problem: weak, strong and classical solutions

On a mixed partial Caputo derivative and its applications to a hyperbolic partial fractional differential equation

Hardy–Hénon fractional equation with nonlinearities involving exponential critical growth

Strong stationarity for non-smooth control problems with fractional semi-linear elliptic equations in dimension $$N\le 3$$

Study on the diffusion fractional m-Laplacian with singular potential term